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Properties

Label 39200.2.a.he
Level $39200$
Weight $2$
Character orbit 39200.a
Self dual yes
Analytic conductor $313.014$
Dimension $6$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [39200,2,Mod(1,39200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("39200.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 39200 = 2^{5} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39200.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,-4,0,0,0,0,0,6,0,4,0,-8,0,0,0,4,0,4,0,0,0,-8,0,0,0,-16,0, 0,0,16,0,-4,0,0,0,4,0,16,0,-16,0,4,0,0,0,-16,0,0,0,12,0,12,0,0,0,-12,0, 20,0,12,0,0,0,0,0,0,0,8,0,16,0,8,0,0,0,0,0,16,0,10,0,-20,0,0,0,-48,0,-16, 0,0,0,-8,0,0,0,28,0,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(313.013575923\)
Dimension: \(6\)
Coefficient field: 6.6.28198912.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 20x^{2} - 16x - 4 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 4 q^{3} + 6 q^{9} + 4 q^{11} - 8 q^{13} + 4 q^{17} + 4 q^{19} - 8 q^{23} - 16 q^{27} + 16 q^{31} - 4 q^{33} + 4 q^{37} + 16 q^{39} - 16 q^{41} + 4 q^{43} - 16 q^{47} + 12 q^{51} + 12 q^{53} - 12 q^{57}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.